Solve Using the Quadratic Formula x^2+58=4

$x^{2} + 58 = 4$

Step 1

Move all terms to the left side of the equation and simplify.

Subtract $4$ from both sides of the equation.

$x^{2} + 58 - 4 = 0$

Subtract $4$ from $58$ .

$x^{2} + 54 = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 1$ , $b = 0$ , and $c = 54$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (1 \cdot 54)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

Raising $0$ to any positive power yields $0$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 1 \cdot 54}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 54$ .

Multiply $- 4$ by $1$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 54}}{2 \cdot 1}$

Multiply $- 4$ by $54$ .

$x = \frac{0 \pm \sqrt{0 - 216}}{2 \cdot 1}$

Subtract $216$ from $0$ .

$x = \frac{0 \pm \sqrt{- 216}}{2 \cdot 1}$

Rewrite $- 216$ as $- 1 (216)$ .

$x = \frac{0 \pm \sqrt{- 1 \cdot 216}}{2 \cdot 1}$

Rewrite $\sqrt{- 1 (216)}$ as $\sqrt{- 1} \cdot \sqrt{216}$ .

$x = \frac{0 \pm \sqrt{- 1} \cdot \sqrt{216}}{2 \cdot 1}$

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \frac{0 \pm i \cdot \sqrt{216}}{2 \cdot 1}$

Rewrite $216$ as $6^{2} \cdot 6$ .

Factor $36$ out of $216$ .

$x = \frac{0 \pm i \cdot \sqrt{36 (6)}}{2 \cdot 1}$

Rewrite $36$ as $6^{2}$ .

$x = \frac{0 \pm i \cdot \sqrt{6^{2} \cdot 6}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{0 \pm i \cdot (6 \sqrt{6})}{2 \cdot 1}$

Move $6$ to the left of $i$ .

$x = \frac{0 \pm 6 i \sqrt{6}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{0 \pm 6 i \sqrt{6}}{2}$

Simplify $\frac{0 \pm 6 i \sqrt{6}}{2}$ .

$x = \pm 3 i \sqrt{6}$